New formulations and efficient algorithms for multichannel NMF

This paper proposes new formulations and algorithms for a multichannel extension of nonnegative matrix factorization (NMF), intending convolutive sound source separation with multiple microphones. The proposed formulation employs Hermitian positive semidefinite matrices to represent a multichannel version of nonnegative elements. Such matrices are basically estimated for NMF bases, but a source separation task can be performed by introducing variables that relate NMF bases and sources. Efficient optimization algorithms in the form of multiplicative updates are derived by using properly designed auxiliary functions. Experimental results show that two instrumental sounds coming from different directions were successfully separated by the proposed algorithm.